Loss Function Computation And Gradient Backpropagation

Multi-backend Keras

Unique: Implements loss functions as backend-agnostic objects in keras/src/losses/ with automatic gradient computation through the active backend's autodiff system. Loss computation and backpropagation are handled transparently during training without user code, leveraging JAX's jax.grad, PyTorch's autograd, or TensorFlow's GradientTape.

vs others: Unlike PyTorch (requires manual loss computation and backpropagation) or TensorFlow (loss functions are TensorFlow-specific), Keras provides a unified loss system across all backends with automatic gradient computation and built-in loss functions for common use cases.

via “backpropagation algorithm derivation and implementation”


Unique: Derives backpropagation from first principles using the chain rule, then shows the computational implementation that makes it efficient (storing activations, computing gradients in reverse topological order), making the connection between mathematical theory and practical algorithm explicit

vs others: More rigorous mathematical treatment than most tutorials, more accessible than academic papers, and includes working code alongside derivations unlike pure theory courses

via “loss function design and implementation”


Unique: Emphasizes numerical stability in loss computation (e.g., log-sum-exp trick for cross-entropy) and the relationship between loss function design and optimization dynamics, showing how loss properties affect gradient flow

vs others: More rigorous than framework documentation by explaining the mathematical foundations and numerical considerations, enabling custom loss design for specialized problems

via “gradient-computation-and-backpropagation”

A guide to building your own working LLM, by Sebastian Raschka.

Unique: Walks through gradient computation step-by-step for each component, showing how chain rule applies through attention and FFN layers, and explains numerical stability tricks (gradient clipping, normalization)

vs others: More educational than relying on framework autograd, enabling practitioners to understand and debug gradient flow issues in custom architectures

via “loss-function-optimization-intuition”


Unique: Visualizes loss landscapes and gradient descent trajectories to show how loss functions guide optimization, making the abstract concept of 'minimizing error' concrete and observable. Videos show why different loss functions produce different gradient signals and learning dynamics.

vs others: More intuitive than mathematical definitions, and more comprehensive than brief mentions in general ML courses or documentation